Integral bases for TQFT modules and unimodular representations of mapping class groups

Abstract

We construct integral bases for the SO(3)-TQFT-modules of surfaces in genus one and two at roots of unity of prime order and show that the corresponding mapping class group representations preserve a unimodular Hermitian form over a ring of algebraic integers. For higher genus surfaces the Hermitian form sometimes must be non-unimodular. In one such case, genus 3 and p=5, we still give an explicit basis.

Cited by in corpus (6)

• A unified Witten-Reshetikhin-Turaev invariant for integral homology spheres
• Integral TQFT for a one-holed torus
• All finite groups are involved in the Mapping Class Group
• Congruence and similarity of 3-manifolds
• Maslov index, Lagrangians, Mapping Class Groups and TQFT
• Heegaard genus, cut number, weak p-congruence, and quantum invariants